J. Cent. South Univ. Technol. (2011) 18: 800−808 DOI: 10.1007/s11771−011−0765−8
ARROW-WTCP: A fast transport protocol based on explicit congestion notification over wired/wireless networks WANG Jian-xin(王建新), LI Jing(李婧), RONG Liang(荣亮) School of Information Science and Engineering, Central South University, Changsha 410083, China © Central South University Press and Springer-Verlag Berlin Heidelberg 2011 Abstract: An explicit congestion notification (ECN)-based distributed transport protocol, ARROW-WTCP (AcceleRate tRansmission towards Optimal Window size TCP for Wireless network), was proposed. The ARROW-WTCP enables feasible deployment of ARROW-TCP from wired to wireless networks by providing a joint design of source and router algorithms. The protocol obtains the actual capacity of the wireless channel by calculating the queue variation in base station (BS) and adjusts the congestion window by using the feedback from its bottleneck link. The simulation results show that the ARROW-WTCP achieves strong stability, max-min fairness in dynamic networks, fast convergence to efficiency without introducing much excess traffic, and almost full link utilization in the steady state. It outperforms the XCP-B (eXplicit Control Protocol Blind), the wireless version of XCP, in terms of stability, fairness, convergence and utilization in wireless networks. Key words: ARROW-WTCP; transport protocol; stability; convergence; fairness; IEEE 802.11
1 Introduction With the progress in wireless technology, the wireless network has become a potential candidate for constructing a broadband wireless backbone. The traditional transmission control protocol (TCP) [1] suffers fairness and efficiency problems, hence degrading the overall quality of service (QoS) of wired/wireless networks. Various protocols for improving the performance of wired/wireless heterogeneous network have been proposed. These include 1) Automatic Repeat-reQuest (ARQ) mechanisms proposed in wireless link layer, such as snoop [2] and ELN [3]; 2) Explicit congestion notification (ECN)-based transport protocol collaborated with routers in the network layer, such as WXCP [4], XCP-B [5] and Jersey [6]; 3) End-to-end congestion control protocols in the transport layer, such as TCP Vegas [7], Packet Pair flow control [8], Veno [9], TCP Westwood [10−12] and Tibet [13]. In end-to-end congestion control protocols, the network is considered as a black box. The loss is detected and round-trip time (RTT) is calculated by monitoring ACKnowledge (ACK) packet [14], and the congestion window is adjusted accordingly. Knowing little about the load information within the network, it is impossible for the protocols to achieve an equitable distribution of network resources. Thus, the end-to-end
congestion control protocols are unstable in dynamic networks. In explicit-feedback-based congestion control mechanism, the source participates in congestion control in collaboration with the intermediate routers. XCP [15−18] is a typical explicit feedback congestion control protocol for the wired networks. It explicitly announces to the sender how much to increase or decrease the congestion window so as to achieve fairness in sharing of network resources. The XCP-B extends XCP for sharedaccess, multi-rate wireless network [19]. The available bandwidth of the wireless channel is calculated from queue variation of base station. The XCP-B can obtain better stability, fairness, convergence, lower queuing delay and higher bandwidth utilization compared with other transmission control protocols in wireless networks, but it becomes inefficient over highly dynamic wireless networks. The ARROW-TCP [20] is based on an explicit rate pre-assignment mechanism. It achieves both strong stability and fast convergence to efficiency and fairness without introducing much excess traffic into networks. Meanwhile, it obtains zero packet loss, zero queuing delay, and full link utilization in the steady state. In shared-access multi-rate media, such as IEEE 802.11, knowing the actual capacity of the channel may be difficult. The computation of the spare capacity is similarly difficult, therefore the ARROW-TCP will not
Foundation item: Projects(60873265, 60903222) supported by the National Natural Science Foundation of China; Project(IRT0661) supported by the Program for Changjiang Scholars and Innovative Research Team in University of China Received date: 2010−03−03; Accepted date: 2010−05−04 Corresponding author: WANG Jian-xin, Professor, PhD; Tel: +86−731−88830212; E-mail:
[email protected]
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work in such media. A modified ARROW-TCP source and router algorithm, named ARROW-WTCP, is proposed, which enables the use of ARROW-TCP in shared-access multi-rate media, thus allowing the advantages of ARROW-TCP to be enjoyed in network paths with shared-access multi-rate bottlenecks.
2 ARROW-WTCP 2.1 Review of ARROW-TCP The ARROW-TCP [20] is a distributed timer-driven congestion control protocol, which is designed for the high bandwidth-delay product networks. In the ARROW-TCP design, it joins the source and router algorithms. Each source utilizes the fair rate calculated by its bottleneck router to update window size and employs link price to manage bottleneck membership. Sources and routers calculate the window size and the fair rate in the same control interval, respectively, which is distinct from the event-driven protocols like TCP. The window size is the amount of data segments to be sent in a constant control interval. The function module in the source is separated into three components, i.e., window control, burstiness control and bottleneck link management. 1) Window control Source uses the feedback from its bottleneck link to update its congestion window periodically with an interval Δ. The evolution of the congestion window is described by s wr (k + 1) = wr (k ) + α ⋅ [ wr* (k − dlr ) − wr (k − d r )] (1) where wr(·) (in number of packets) is the congestion window, α is a control gain, and wr∗ is the desired optimal sending window that relies on the fair rate gl from the bottleneck link l. The fair rate gl is the desired amount of resource shared by the bottlenecked flows r of link l. The RTT dr is the sum of the forward delay d s lr to its bottleneck link r l sand the backward delay d lr from link l, i.e., d r = d lr + d lr . The optimal window size is calculated as wr∗ (k ) =
gl (k ) ∗ Δ sr
(2)
where sr (in bit) is the packet size. 2) Burstiness control Source sends all data packets evenly over the interval Δ so as to avoid a burst. 3) Bottleneck link management It takes charge of switching and confirmation of the bottleneck link. The router algorithm is also divided into three components, i.e., calculation of the fair rate, the link
price, and the estimation of the number of bottleneck flows. 1) The router computes fair rate for its bottleneck flows by dividing the residual bandwidth γlCl−ul(k) equally among all bottleneck flows Nl. The fair rate gl(k) is calculated in the time interval Δ:
gl (k ) =
γ l Cl − ul (k ) Nl (k )
(3)
where γ l is the target link utilization, γ l ≤ 1 , Cl is the associated link capacity, Cl>0 (in bit/s), and ul is the aggregate rate of its unbottlenecked flows. 2) Routers communicate with the sources through link price. The link price, pl, is used to indicate the link congestion level to its bottleneck flows: pl (k ) =
yl (k ) − γ l Cl yl (k )
(4)
where yl (in bit/s) is the aggregate rate of all flows which use link l. Initially, the source r considers the router with the maximum link price in its route as the bottleneck. When the system reaches the steady state, there may be multiple routers with zero link price in the route of source r. In this case, the router with the smallest fair rate is considered as the bottleneck of source r. This is shown by the result in Ref.[21] which states that, for each network, there is a max-min rate allocation. 3) The estimation of the number of bottleneck flows Nl(k) is computed as ⎛ (1−θ ) wr ( k )
∑ ⎜⎜ ∑
r∈S lc ⎝
i =1
θ wr ( k +1) ⎞ 1 1 + ∑ ⎟ = Nl ⎟ wr (k ) j =1 wr ( k + 1) ⎠
(5)
The stable region of α in Eq.(1) is obtained by the Routh-Hurwite stability criterion and the fact that the ARROW-TCP achieves both strong stability and fast convergence through simulations is demonstrated. However, there are situations where the capacity estimation error may be considerable, such as the case of half-duplex, shared-access links and multi-rate wireless channels. The IEEE 802.11 is one example of this type of transmission media. Estimating the total capacity of the IEEE 802.11 channel is non-trivial, as it depends on the number of collisions, handshake (RTS/CTS), fragmentation thresholds, average packet size and data rates used by each station. It is even harder to know the bandwidth assigned to each of the stations, as it depends on the number of currently active stations. ARROW-TCP cannot estimate the available bandwidth of the wireless channel, which leads to long queue delay and overflow in BS, and error estimation of the number of the bottleneck flows. Besides, the ARROW-TCP cannot deal with the wireless packet loss.
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2.2 Design of ARROW-WTCP The modifications to the ARROW-TCP algorithm is proposed to overcome the difficulties of ARROW-TCP operating in shared-access, half-duplex media. The modified algorithm is named ARROW-WTCP. The new algorithm only needs to be deployed in the nodes where capacity is variable and it inter-operates with the ARROW-TCP. The biggest concern in wireless network is how to let a bottleneck controller know the exact capacity of the channel, and the capacity occupied by each station. The first modification in the new algorithm is the calculation of the spare bandwidth of the channel. Instead of calculating the difference between the channel capacity and the input bandwidth, the spare bandwidth is calculated from the queue variation on each control interval: q& (t ) = y (t ) − C
(6)
where q& (t ) is the differential of the queue length. 1) Router algorithm Generally, it assumes that the wireless link is the bottleneck for the connection over hybrid wired and wireless networks. With the development of MIMO OFDM technology for the next generation wireless LAN, the transfer rate is upgraded from 54 Mbit/s, 108 Mbit/s to 300 Mbit/s even as high as 600 Mbit/s. WLAN is not considered as the bottleneck as before. The base station (BS) computes the fair rate for its bottleneck flows by dividing the residual bandwidth equally among all bottleneck flows. The residual bandwidth can be calculated from the queue variation on each control interval Δ: ⎧ q0 ⎪ N (k ) ⋅ Δ , if q = 0 ^ Δq = 0 ⎪⎪ l gl (k ) = ⎨ Δq q ( k ) − q* −β ⋅ ] − ul (k ) ⎪ γ l ⋅ [ yl (k ) − Δ Δ ⎪ , if q > 0 Nl (k ) ⎪⎩ (7) When there is a zero queue, in other words, when the channel is under-utilized, the ARROW-WTCP router feeds back a fixed amount of rate at each control interval. The amount is chosen so that the bottleneck queue does not drop packets in the subsequent control interval. q0 is a constant. By setting q0=8, better performance in the simulation experiments is obtained. When there is a non-zero queue, i.e., the channel is saturated, a different feedback function for the fair rate is adopted. In Eq.(7), Δq is the difference between the values of the persistent queue in the current and the last control interval, q* is the desired optimal queue length at which the queue will
stabilize, and β is the design parameter. Due to the randomness of the access in a shared-access medium and the transitory response of the system, the queue length in the wireless nodes cannot be stabilized at zero but fluctuate in a small range. Set q*=40 and β=0.05. In addition to calculating the fair rate, the link prices are calculated as ⎧−1, if q = 0 ^ Δq = 0 ⎪ pl (k ) = ⎨ γ l ⋅ (q − q*) , if q > 0 ⎪(1 − γ l ) + y⋅Δ ⎩
(8)
For source, the router with the maximum link price in its route is considered as the bottleneck initially. When the length and the variation of the queue in BS are zero, the link price of the wireless channel is set to −1. It will be the maximum link price in route. When there is a non-zero queue, the link price formula is shown in Eq.(8). There are different algorithms of link price for wired links and wireless channel. The algorithm on wired links is the same as the ARROW-TCP. Calculating the number of the bottleneck flows is very important in router algorithm, especially for the BS. Based on the fact that both sources and routers operate in the control interval Δ and each source sends out packets in a fluid-like manner by spacing the outgoing packets evenly over Δ time, it is not difficult to derive that, for any link, the packets arriving during an interval are generally originated from their sources in two consecutive intervals. For example, supposing that source r is bottlenecked by link l, the control interval of link l can be separated by a time demarcation where packets arriving before and after the demarcation are originated from the k-th and (k+1)-th interval of source r. Use a fraction θ to represent the time demarcation which separates the control interval of link l into (1−θ)Δ and θΔ. Since packets are sent in a fluid-like manner with inter-packet interval, the number of arrival packets from source r in (1−θ)Δ and θΔ time are (1−θ)wr(k) and θwr(k+1), respectively. Therefore, for each packet arriving at link l over a control interval Δ, there is (1−θ ) wr ( k )
∑ i =1
θ wr ( k +1) 1 1 + ∑ =1 wr (k ) wr (k + 1) j =1
(9)
Generalizing the case to all Nl flows bottlenecked by link l yields Eq.(5). In the ARROW-WTCP router algorithm, it cannot make the equilibrium queuing delay zero but varies in a small range. Therefore, the algorithm of computing the number of bottleneck flows is also correct for the ARROW-WTCP. 2) Source algorithm The source uses the feedback of the bottleneck link to update its congestion window. The evolution of the congestion window is described as
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⎧ wr (k ) + q0 / Nl (k ), if pl = −1 s ⎪ wr (k + 1) = ⎨ wr (k ) + α ⋅ [ wr* (k − dlr ) − wr (k − d r )], ⎪ if pl ≠ −1 ∨ bnck_time = 0 ⎩
803
(10)
A fixed amount value is added by the original congestion window when the link price in the ACK is −1, which means that the channel is under-utilized. It is equivalent to Additive-Increase (AI) phase in the traditional TCP. When the link price is not equal to −1, i.e., the wireless channel is saturated, the congestion window adjustment algorithm is the same as that of the ARROW-TCP. When the congestion window is less than the desired optimal sending window, it will be increased with the integral rate. Once it exceeds the desired optimal value, the ARROW-WTCP will reduce the size of the congestion window to approximately the desired optimal one. If the congestion window is equal to the desired optimal value, it means that it is in the stable status that should be maintained. The desired optimal sending window, wr* , is computed on the fair rate according to Eq.(2). Besides, the source identifies whether or not IEEE 802.11 hop is the bottleneck of the network by reading RC and RS in the ACK. RC is the current hop number and is incremented by each router, and RS is modified by the routers which perceive their link price to be higher than that experienced by the flow at the preceding routers. If the value of RS equals RC, the source identifies that the bottleneck is on the last hop. Therefore, the source adopts the algorithm described above. Otherwise, the source adjusts the congestion window as that of the ARROW-TCP.
3 Stability analysis In the stability analysis of ARROW-TCP, the control parameter, α in Eq.(1), is related to the number of the periodicity in RTT delay alone for the asymptotic stability of source r. This is proved by the Routh-Hurwitz stability criterion, and the correctness is validated through the Nyquist stability criterion in Ref.[20]. The stability analysis of parameter α is still correct for the stability of ARROW-WTCP. The ARROW-WTCP improves the algorithms of computing fair rate and link price. It introduces the desired optimal queue length q* and the parameter β. Let ri(t) be the sending rate of user i at time t, then the aggregate traffic rate is y(t)=Σri(t). Since the input traffic rate is y(t)=Σwi(t)/Δ, the derivative of the traffic rate y& (t ) is y& (k ) = −
s α α β ⋅ q& (k − d r ) − ⋅ ⋅ [q (k − dlr ) − q* ] Δ Δ Δ
(11)
There is a precondition for Eq.(11), i.e. the wireless hop is the bottleneck link for all flows. Therefore, the
aggregate rate of the unbottlenecked flows, ul(k), on the wireless channel equals zero. Change variable to x(t ) = q& (t ) = y (t ) − C , and Eq.(12) can be obtained from Eq.(11): x& (k ) = −
s α α β ⋅ x(k − d r ) − ⋅ ⋅ [q(k − dlr ) − q* ] Δ Δ Δ
(12)
As shown in Fig.1, the system can be expressed using a delayed feedback model.
Fig.1 Time-delay feedback control system
In Fig.1, K1=α/Δ, K2=β/Δ, and the open-loop transfer function of the closed-loop system is s K1 ⋅ K 2 ⋅ exp(−dlr s ) G( s) = (13) s[ s + K1 ⋅ exp(−d r s)]
To maintain the stability of the system, the characteristics of the amplitude−frequency and phase− frequency of the open-loop transfer function are explored, and the range of β is obtained. The Nyquist plots with β=0.02, 0.04, 0.05, 0.08, as given in Fig.2, do not encircle −1. With the larger value of β, the plot is farther away from the point (−1, 0). Figure 3 shows the differential of the bottleneck queue evolution trajectory. The bottleneck queue length finally converges to the steady state monotonically. The simulation results validate that the closed-loop system will converge to stationary. When setting β=0.05, the performance of simulation is better.
Fig.2 Nyquist plot of open-loop transfer function
4 Performance 4.1 Scenario The performance of ARROW-WTCP is validated in
804
J. Cent. South Univ. Technol. (2011) 18: 800−808 Table 1 IEEE 802.11b MAC and PHY layer parameters Parameter Value Preamble length/bit
72
PLCP header length/bit
48
PLCP data rate/(Mbit·s−1)
1
Basic rate/(Mbit·s−1)
1
−1
Fig.3 Queue dynamics with different configurations of β
ns2-2.29 simulator, which is implemented on the top of the original ns-2 XCP-B implementation. As shown in Fig.4, the simulations work on wired/wireless hybrid network scenarios. When simulating the ARROW-WTCP, only the queues attached to the 802.11 medium use the ARROW-WTCP router algorithm. All queues attached to wired links use the original ARROW-TCP router algorithm. The wireless nodes use the 802.11 MAC DCF mode with RTS/CTS disabled for all the packets. The data rate is set to be 11 Mbit/s and the basic rate is set to be 1 Mbit/s by default in wireless medium. The packet size is set to be 1 400 bytes by default, the buffer size Q=100, q0=8, q*=40, β=0.05, α=0.4, and the time interval Δ=100 ms.
Fig.4 Single-bottleneck topology with one IEEE 802.11 hop
The basic parameters in the 802.11 MAC DCF mode are listed in Table 1. The throughput of the wireless network can be expressed by Ps Pt,r E[ P] S= (14) (1 − Pt,r )σ + Pt ,r Ps ts + Pt,r (1 − Ps )tc where Pt,r is the probability of at least one frame transmission in a slot, Ps is the probability of successful transmission, ts is the time needed for a successful transmission, tc is the time wasted by a conflict, E[P] is the average data frame length, and σ is the length of a time slot. Let n be the number of the wireless nodes, and the formula of the effective throughput of the wireless networks is S (15) G= n +1
Data rate/(Mbit·s )
11
Slot time/μs
20
Short inter-frame space/μs
10
DCF inter-frame space/μs
50
Minimum congestion window
31
Maximum congestion window
1 023
RTS threshold/byte
2 500
ShortRetryLimit
7
LongRetryLimit
4
−1
Bandwidth/(Mbit·s )
11
ACK frame
112 bits + PHY Header
DSF—Distributed coordination function
where S is the normalized system throughput. According to the above formulas, the upper bound of the effective throughput for UDP flows is 5.4 Mbit/s in theory, while the actual effective throughput is between 4.5 Mbit/s and 4.9 Mbit/s when considering the conflict avoidance and back-off in the wireless channel. When the 802.11 hop is the bottleneck of the network, the throughput is between 4.5 Mbit/s and 4.9 Mbit/s. When the bandwidth of one wired link is set to be 4 Mbit/s, the queue length in BS becomes zero and the maximum throughput is 4 Mbit/s, which infers that the bottleneck is on the wired link by analyzing the results. 4.2 Simulation 1) Experiment 1: Convergence under singlebottleneck topology The convergence, stability and fairness of ARROW-WTCP and XCP-B are examined under the single-bottleneck topology, as shown in Fig.4. Start one flow every 50 s, from t=0 s until three flows have been started. At t=200 s, terminate one flow every 50 s. The simulation runtime is 300 s. The access delay of the three flows is 10, 20 and 30 ms, respectively. The bandwidth of the wired link between the router R(0) and R(1) is set to be 10 Mbit/s, and the bandwidth between R(1) and BS(0) is set to be 50 Mbit/s. Two links have propagation delay of 20 ms. The 802.11 hop becomes the bottleneck. Figure 5 presents per-flow throughput of each flow and the queue length of BS. The bandwidth of the wired link between the routers R(0) and R(1) is set to be 4 Mbit/s. The wired link between R(0) and R(1) becomes the bottleneck. The throughputs of the two protocols are shown in Fig.6.
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Fig.5 Convergences of ARROW-WTCP and XCP-B under bottleneck in 802.11 hop: (a), (b) Rate; (c), (d) Queue length of BS; (a), (c) ARROW-WTCP; (b), (d) XCP-B
Fig.6 Convergences of ARROW-WTCP and XCP-B under bottleneck in wired link: (a) ARROW-WTCP; (b) XCP-B
The per-flow throughput and the queue length in the bottleneck link are used as the performance measures. As shown in Fig.5 and Fig.6, the ARROW-WTCP obtains better convergence and stability under the condition of multi-flow co-existence. Both ARROW-WTCP and XCP-B achieve almost full link utilization no matter the bottleneck is in the wired or wireless link. As shown in Fig.5(c), there is queue building-up in a short time when the flows enter or exit; however, the queue length is within the size of the bottleneck buffer.
2) Experiment 2: Transient behavior under singlebottleneck topology The convergence and transient behavior of the protocols are examined in the presence of burst traffic in this experiment. Flow 1 with RTT of 400 ms starts at t= 0 s, and additional four flows with RTT of 10 ms join together at t=50 s. The simulation runtime is 100 s. The topology is shown in Fig.4. The bandwidth of the wired link between R(0) and R(1), between R(1) and BS(0) are set to be 50 Mbit/s, and
806
the propagation delay is 1 ms, so the 802.11 hop becomes the bottleneck. The bandwidth between R(0) and R(1) is set to be 4 Mbit/s, then the bottleneck is on the wired link. Figures 7(a) and 8(a) present the per-flow throughput and the total throughput of all flows. The ARROW-WTCP can eliminate capacity overshooting and converge to steady throughput after new flows enter and all flows share the link bandwidth fairly. As shown in Fig.7(c), the queue length increases quickly after new flows enter, but it varies within a smaller range. The simulation results in Fig.7(b) and Fig.8(b) show that the XCP-B exhibits unstable throughput trajectory. The
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reason is that the stability of XCP-B is related with RTT and buffer size. 3) Experiment 3: Stability in presence of mice flows under single-bottleneck topology In this experiment, the stability of elephant flows which are affected by the random arrival/departure mice flows is investigated. Flow 1 with RTT of 400 ms and flow 2 with RTT of 100 ms start the transmission at t=0 s and t=10 s, respectively. From t=20 s, 100 mice flows join. The simulation runtime is 200 s. The number of active flows at any instant time is plotted in Fig.9(a). The topology is
Fig.7 Transient behaviors of ARROW-WTCP ((a), (c)) and XCP-B ((b), (d)) under bottleneck in 802.11 hop: (a), (b) Rate; (c), (d) Queue length of BS
Fig.8 Transient behaviors of ARROW-WTCP (a) and XCP-B (b) under bottleneck in wired link
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Fig.9 Stabilities of ARROW-WTCP ((b), (d)) and XCP-B ((c), (e)) in presence of mice flows under bottleneck in 802.11 hop: (a) Number of active sessions; (b), (c) Rate; (d), (e) Queue length of BS
shown in Fig.4. The bandwidth between R(0) and R(1) is set to be 50 Mbit/s with 30 ms propagation delay, and the bandwidth between R(1) and BS(0) is 80 Mbit/s with 20 ms propagation delay. The simulation results are shown in Fig.9. The stability of XCP-B is very poor in the presence of the random mice flows. The elephant flows cannot stabilize their throughputs even if the mice flows depart from the network. ARROW-WTCP obtains satisfactory stability and fair allocation in dynamic environment, but it generates packets loss in the presence of random mice
flows owing to small buffer size. However, there are no packet losses after the random flows depart from the network for ARROW-WTCP but not for XCP-B.
5 Conclusions 1) A fast transport protocol ARROW-WTCP is proposed for the multi-access, channel sharing wireless network. It allows the advantages of ARROW-TCP to be enjoyed in such networks. The improvements consist of the source and router algorithms under two conditions,
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i.e., saturated and under-utilized wireless channel. 2) A time-delay feedback control model is set up, which proves the stability of ARROW-WTCP. The value of parameter β is obtained through the theoretical analysis and simulation experiments. 3) The algorithms are extensively tested through simulation in the network scenario including one IEEE 802.11 hop as well as wired links. The ARROW-WTCP maintains stability, fairness, convergence, and high utilization. It outperforms the XCP-B in terms of stability, convergence and transient behavior in random mice flows and burst traffic scenarios.
[10]
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